Solve for $x$ and $y$ using elimination. $\begin{align*}5x+8y &= 3 \\ -4x-4y &= -1\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $2$ $\begin{align*}5x+8y &= 3\\ -8x-8y &= -2\end{align*}$ Add the top and bottom equations. $-3x = 1$ Divide both sides by $-3$ and reduce as necessary. $x = -\dfrac{1}{3}$ Substitute $-\dfrac{1}{3}$ for $x$ in the top equation. $5( -\dfrac{1}{3})+8y = 3$ $-\dfrac{5}{3}+8y = 3$ $8y = \dfrac{14}{3}$ $y = \dfrac{7}{12}$ The solution is $\enspace x = -\dfrac{1}{3}, \enspace y = \dfrac{7}{12}$.